We examine the socially optimal wealth distribution in a two-person two-good model with heterogeneous workers and asymmetric social interactions where only one (social) individual derives positive or negative utility from the leisure of the other (non-social) individual. We show that the interdependence can effectively counter-act the need to transfer wealth to low-wage individuals and may require them to be poorer by all objective measures. We demonstrate that in the presence of social interactions it can be socially desirable to keep substantial wealth inequality.